Find the value of Sin-1x + Cos-1x where x e [-1,1] В. п c. А. 1 D. 0

Q: nd all values of x in the interval [0, 2x] that satisfy the equation. (Enter your an 9 sin(2x) = 9…

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Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

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Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: The coefficient of Sin(x) in the antiderivative of F(x) =| cos is 17/16

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Q: 4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

A: This integration can be integrated by using substitution method. Clearly it is observable that put…

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

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Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: 4. Evalaute cos(x) sin(x) dx

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Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

A: Consider finding the root of f(x) = e-x(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: apply Newton’s Method to f and initial guess x0 to calculate x1, x2, x3. f (x) = cos x − 4x, x0 = 1

A: Given: Calculate-

Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

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Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: Sketch the following between x = 0 and x = 4 pi      y =  sin x + cos 2 x

A: Given: The function is  y =  sin x + cos 2 x

Q: Suppose m and n are constants and m‡ n. 1. Evaluate sin(mx) cos(nx) dx

A: using trigonometric identity

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: S cosx. sin“x. dx = cos³x + C sinx + C O None O sin*x 4 + C

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Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

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Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

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Q: 4) Find when y? – x² + cos(x + y) = 0

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: Evaluate in x cos x dx. .3 I COS" T

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Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

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Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

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Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

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Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

A: I am attaching image so that you understand each and every step.

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

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Q: 1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

A: Given query is to find cos(x+y) and sin2y.

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

A: Given: fx=sinxcos3xf'x=cos4x-2sinxsin3x To find: f''π3=?f'''π3=? Formulas used:…

Q: Solve for x where 0 <x < 2n. a) cos (a + ] V2 sin æ b) 5 cos? x – 13 sin x +1 = 0

A: a) The given equation is cosx+π4=2sinx. Solve the above equation as follows. cosx+π4=2sinxcosx…

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B }sin'x + C {c}-cos'x + C {D} sin 2x + C

A: Given query is to find the incorrect option for the integral.

Q: 1) fcoe cos x sin rdr

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Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

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Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: a sin a + In v ) da + tan adv = 0 Cos a

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Q: Using an appropriate substitution, f sin®(x)cos³(x)dx is equal to:

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below